Semileptonic decays of BcB_c meson to S-wave charmonium states in the perturbative QCD approach

Inspired by the recent measurement of the ratio of $B_c$ branching fractions to $J/\psi \pi^+$ and $J/\psi \mu^+\nu_{\mu}$ final states at the LHCb detector, we study the semileptonic decays of $B_c$ meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions $B_c\rightarrow P,V$, where $P$ and $V$ denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for $B_c$ meson. It is found that the predicted branching ratios range from $10^{-6}$ up to $10^{-2}$ and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions $\frac{\mathcal {BR}(B_c^+\rightarrow J/\Psi \pi^+)}{\mathcal {BR}(B_c^+\rightarrow J/\Psi \mu^+\nu_{\mu})}$ is in good agreement with the data. For $B_c\rightarrow V l \nu_l$ decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.Comment: 12 pages, 3 figures, 5 table

3-(4-Carb­oxy-5-carboxyl­ato-1H-imidazol-2-yl)pyridin-1-ium monohydrate

In the zwitterionic mol­ecule of the title compound, C10H7N3O4·H2O, one carboxyl group is deprotonated and the pyridine N atom is protonated. The pyridinium and imidazole rings form a dihedral angle of 5.23 (1)°. An intramolecular O—H⋯O hydrogen bond occurs. In the crystal, inter­molecular N—H⋯O, O—H⋯N and O—H⋯O hydrogen bonds link the zwitterions and water mol­ecules into sheets parallel to (102)

2-(2-Hy­droxy-3-meth­oxy­phen­yl)-1H-benzimidazol-3-ium perchlorate

In the title mol­ecular salt, C14H13N2O2 +·ClO4 −, the ring systems in the cation are almost coplanar [dihedral angle = 5.53 (13)°]. Intra­molecular N—H⋯O and O—H⋯O hydrogen bonds generate S(6) and S(5) rings, respectively. In the crystal, the two H atoms involved in the intra­molecular hydrogen bonds also participate in inter­molecular links to acceptor O atoms of the perchlorate anions. A simple inter­molecular N—H⋯O bond also occurs. Together, these form a double-chain structure along [101]